The app world update is broken. So far there is nothing you can do to resolve it. I even found and tried to install an old version and it would not work. Hundreds of complaints on the web with the same problem but RIM has said nothing yet.
Sorry for the bad news but all we can do is wait.
Welcome to BlackBerry

Replacing it with the older version has worked for most.
This is so ridiculous, I have the solution, but this page won't let me paste the link!!! Grrrrr!
If you know about BBH plus.net, maybe google it, then it has the earlier version of App world, you can replace it.

If anyone has Facebook, the full explanation is on my status (Nawaar Railoun)

I just did an upgrade to BB App World 3.1.0.58. It installed fine, rebooted as it should after install process completes, no errors on reboot, but I have No Icon on my home screen to launch the app. It is not hidden, it did not get put in a rogue folder. I even unistalled reinstalled 3.1.0.56 from m.blackberry.com and then updated when the update notice came in. Same problem.. No icon to launch the app.